I am using emmeans to produce estimated marginal means from GLMMs with Poisson or negative binomial distributions, but for a few of my models the confidence interval is in the negative. I was not expecting this given the distribution. Can I simply set the lower bound to zero, or am I missing something?

m1<-glmmTMB(count ~ treatment + (1|nestBoxSlot), data=data, offset=log(noIndividual), ziformula=~1, family="nbinom2")

emmean <- emmeans(m1, "treatment", type="response", offset=0)

Result of emmean

  treatment  response        SE  df   lower.CL   upper.CL
1         C 8.1624947 8.0114700 528 -7.5757742 23.9007636
2         M 0.2043217 0.2637268 528 -0.3137608  0.7224043
3        MD 0.4341052 0.5491020 528 -0.6445876  1.5127979

This can happen if your software back-transforms the estimates before computing the intervals, and then uses the SEs of the back-transformed estimates (usually obtained by the delta method). You can avoid this by computing the intervals on the link scale (e.g., log), and then back-transforming the endpoints.

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    $\begingroup$ BTW, the latter is what the emmeans R package does by default. So I am not sure how this happened. Can you show the code you used, and the results? $\endgroup$
    – Russ Lenth
    May 10 '20 at 12:55
  • $\begingroup$ Indeed, that is why I was confused. Edited above with an example. $\endgroup$ May 10 '20 at 16:02
  • $\begingroup$ Odd. Can you tell if the answers are reasonable? What do you get on the link scale? And keep in mind that the estimates don't include the ZI part, I believe. (However, if Ben has revamped it to include the ZI part and estimate the mean response, that would involve back-transforming, and would explain everything. $\endgroup$
    – Russ Lenth
    May 10 '20 at 16:46
  • $\begingroup$ The estimated response is reasonable, but these are counts of seconds. When I set zero inflation to 0 they are considerably less into the negative. $\endgroup$ May 10 '20 at 16:58
  • $\begingroup$ I have not been able to find out how emmeans handles calculating CI from zero inflation models in glmmTMB $\endgroup$ May 12 '20 at 16:49

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